Minimization of Spread of Time-Constants and Scaling Factors in Fractional-Order Differentiator and Integrator Realizations

  • Stavroula Kapoulea
  • Costas Psychalinos
  • Ahmed S. Elwakil
Short Paper


The approximations of fractional-order differentiator/integrator transfer functions are currently performed using integer-order rational functions, which are in general implemented through appropriate multi-feedback topologies. The spreading in the values of time-constants and scaling factors, needed to implement these topologies, increases as the order of the differentiator/integrator and/or the order of the approximation increases. This leads to non-practical values of capacitances and resistances/transconductances in the implementation. A solution to overcome this obstacle is introduced in this paper, based on the employment of a combination of fractional-order and integer-order integrators and differentiators for implementing the desired function. The performance of the proposed scheme is verified through post-layout simulations using Cadence and the Design Kit provided by the Austria Mikro Systeme \(0.35~\upmu \mathrm{m}\) CMOS technology process.


Fractional-order circuits Fractional-order integrators Fractional-order differentiators Operational transconductance amplifiers CMOS analog integrated circuits 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Electronics Laboratory, Physics DepartmentUniversity of PatrasRio PatrasGreece
  2. 2.Department of Electrical and Computer EngineeringUniversity of SharjahSharjahUnited Arab Emirates
  3. 3.Nanoelectronics Integrated Systems Center (NISC)Nile UniversityGizaEgypt

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